Will a outboard engine be damaged if run enxtended period of time hooked uo to a garden hose?

no as long as the water muffs dont slide off water inlet of lower unit,and you have enough water ppressure going to hose, also do not rev up engine unless drive is compketely submerged in test tank. also watch your water circulation hose (the pee hose on top side of engine the lets you know water is pumping through engine. over reving on land will cause water pump to suck air and burn up your pump impeller in seconds. and overheating is the worst thing to do to any motor. ps watch your temp gauge.